Characterization of fractured reservoirs plays an important role in optimizing production from fractured reservoirs. Such characterization may include, for example, determining variations in fracture density and permeability of the fracture network and determining orientation of fractures in the fracture network. Areas of high fracture density can represent “sweet spots” of high permeability and therefore can be targeted for placement of infill wells. Fractures with largest aperture at depth tend to be oriented along the direction of the maximum in-situ horizontal stress and may therefore lead to significant permeability in the reservoir, which would lead to permeability anisotropy. For optimum drainage it is important that infill wells are more closely spaced along the direction of minimum permeability than along the direction of maximum permeability. Fracture orientation is useful in determining trajectory of a deviated well. For maximum recovery, the trajectory of the well can be chosen such that as many fractures as possible are intersected.
It is known that oriented sets of fractures lead to direction-dependent seismic velocities. As a result, use of seismic waves to determine the orientation of fractures has received much attention. For example, Lynn et al. use the azimuthal variation in reflection amplitude of seismic P-waves to characterize naturally fractured gas reservoirs in the Bluebell Altamont Field in the Uinta Basin, Northeastern Utah. (Lynn, H. B. Bates, C. R., Layman, M., and Jones, M. “Natural fracture characterization using P-wave reflection seismic data, VSP, borehole imaging logs, and in-situ stress field determination,” SPE 29595, (1995).) Reflection amplitudes offer advantages over seismic velocities for characterizing fractured reservoirs since they have higher vertical resolution and are more sensitive to the properties of the reservoir. However, interpretation of variations in reflection amplitude requires a model that allows the measured change in reflection amplitude to be inverted for the characteristics of the fractured reservoir.
Current models used to describe the seismic response of fractured reservoirs make simplified assumptions that prevent fractured reservoirs from being characterized correctly. For example, most models assume a single set of perfectly aligned fractures (see, e.g., U.S. Pat. No. 5,508,973 issued to Mallick et al.), while most reservoirs contain several fracture sets with variable orientations within a given fracture set. Use of a model of a fractured reservoir that assumes a single set of fractures in a reservoir containing several fracture sets can give misleading results. For example, consider a vertically fractured reservoir containing a large number of fractures with normals being isotropically distributed in the horizontal plane. For such a fractured reservoir there would be little or no variation in reflection coefficient with azimuth, and an interpretation of the reflection amplitude versus azimuth curve using an assumption of a single set of aligned fractures would predict incorrectly that the fracture density is zero.
From the foregoing, there continues to be a desire for an improved method of characterizing a fractured reservoir using seismic reflection amplitudes.